Monocentric lens-based multi-scale optical systems and methods of use

ABSTRACT

A monocentric lens-based multi-scale imaging system is disclosed. Embodiments of the present invention comprise a monocentric lens as an objective lens that collects light from a scene. Monocentric lenses in accordance with the present invention include a spherical central lens element and a plurality of lens shell sections that collectively reduce at least one of spherical and chromatic aberration from the magnitude introduced by the spherical lens element itself. A plurality of secondary lenses image the scene through the objective lens and further reduce the magnitude of aberrations introduced by the objective lens. A plurality of sensor arrays converts optical sub-images of the scene into a plurality of digital images, which can then be used to form a composite image of the scene.

CROSS REFERENCE TO RELATED APPLICATIONS

This case is a continuation of co-pending U.S. patent application Ser.No. 14/313,233, filed Jun. 24, 2014, which is a continuation of U.S.patent application Ser. No. 13/095,407, filed Apr. 27, 2011 (now U.S.Pat. No. 8,830,377), which claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/328,213, filed Apr. 27, 2010, and which is acontinuation-in-part of U.S. patent application Ser. No. 12/651,894filed Jan. 4, 2010 (now U.S. Pat. No. 8,259,212), which claims priorityto U.S. Provisional Patent Application Ser. No. 61/142,499, filed Jan.5, 2009, each of which is incorporated herein by reference in itsentirety.

FIELD OF THE INVENTION

The present invention relates to optics in general, and, moreparticularly, to imaging systems.

BACKGROUND OF THE INVENTION

A digital camera system is normally based on a lens system comprising anumber of optical elements that image a scene onto an array ofoptoelectronic detector elements. As digital camera systems haveevolved, these optical elements and detector arrays have been becomingprogressively smaller. Unfortunately, angular resolution and number ofresolvable object points typically scale with the size of an imagingsystem. As a result, the optical performance of such camera systemsbegins to suffer as the optical elements and detector elements continueto shrink.

Typically, it is desirable for the lens system to (1) collect as much ofthe light signal as possible over as large an aperture as possible; and(2) process the collected light signal to either form an optical imageon the detector array or to encode the light signal for digital imageestimation. Each detector in the detector array receives light from thelens system and converts it into an electrical signal whose magnitude isa function of light intensity. These electrical signals are thenprocessed to develop a composite digital image of the scene and/orestimate one or more properties of the scene.

Lens system design begins by specifying targets for major performancemetrics, such as angular resolution, field-of-view, depth of field,spectral range, sensitivity, dynamic range, system mass and volume.Angular resolution is generally the most significant initial metric. Thebest angular resolution of a lens is given by λ/A, where λ is theoperating wavelength and A is the collection aperture diameter. Once thecollection aperture size has been determined by this relationship, alens is designed to achieve the remaining performance metrics byjudicious choice of materials and surface profiles.

In conventional lens design, the aperture size of an entrance lens oroptical stop (i.e., the primary aperture) often determines the effectiveaperture size of all subsequent lens surfaces (i.e., the secondaryaperture) in the lens system. The use of multiple lenses and aperturesenables a lens system to simultaneously create an effective focal lengthand magnification appropriate to the imaging task at hand, reduce imageaberrations, and provide correct image orientation. Secondary aperturesare typically matched to the effective cross section of the magnified ordemagnified entrance aperture propagated through the lens system. Insystems with low aberration, the size of the entrance aperture oftendetermines angular resolution of the lens system while the size of thesecondary apertures determines the field-of-view of the lens system.

Simple cameras typically balance field-of-view and resolution by using asequence of lenses having approximately equally sized apertures.Microscopes, on the other hand, achieve large field-of-view and highangular resolution by increasing secondary aperture relative to thecollection aperture. Telescopes achieve extra-ordinary angularresolution with a limited field-of-view by decreasing secondary aperturesize. Wide-field cameras achieve large field-of-view by toleratingsignificant aberration across the image with approximately equal primaryand secondary apertures. Conventional lens design, therefore, normallyrequires trade-offs between desired performance metrics. For example,telescopes achieve high angular resolution by sacrificing field-of-view,wide-field imagers achieve large angular fields-of-view by sacrificingdiffraction-limited angular resolution, and compound-optics camerasachieve high quality by expanding system volume to include moreaberration-correction optics.

In order to overcome some of the limitations of standard imaging optics,multi-aperture cameras have been developed. In multi-aperture systems, astandard camera objective lens is replaced by an array of lenslets,wherein each lenslet has a reduced focal length in comparison to aconventional camera. In such approaches, a detector measures a set ofsub-sampled versions of the object within the field-of-view.Post-processing algorithms are used to generate a high-resolution imagefrom the set of sub-sampled sub-images. The result is reduced systemvolume; however, the reduction in system volume is achieved at the costof significant computational post-processing and compromised imagequality.

In addition, the design space for multi-aperture cameras is severelyrestricted, which has limited their adoption in practical systems. Theuse of a multi-aperture camera requires that the size of its detectorarray and system aperture be approximately the same size. As a result,conventional multi-aperture designs are generally restricted to verysmall collection apertures. This also limits the number of cameraformats that can be designed. Further, a multi-aperture camera typicallyhas a restricted field-of-view due to a need to prevent the overlappingof sub-images on the detector array. Such overlapping can be avoided byintroducing a field stop in the optical design; however, this increasessystem volume. Alternatively, absorbing barriers can be placed betweenthe sub-image regions of the detector array; however, this significantlyincreases manufacturing cost and complexity.

For these reasons, a lens system that avoids some of the designtrade-offs associated with conventional lens design and that achieveshigh performance cost-effectively is desirable.

SUMMARY OF THE INVENTION

The present invention enables optical systems that overcome some of thedisadvantages of the prior art. Specifically, the present inventionenables multi-scale optical system designs based on an objective lensthat is a monocentric compound lens, wherein the objective lens has aspherical geometry and includes a plurality of shell segments.Embodiments of the present invention are particularly well suited foruse in high-altitude surveillance systems and wide-field astronomicalsky surveying systems.

In an optical system in accordance with the present invention, anobjective lens collects light from a scene and images the light at asubstantially spherically shaped image field. A substantiallyspherically shaped arrangement of secondary lenses is located near, butdisplaced from, the image field. Each secondary lens processes lightreceived from the objective lens and images it onto a correspondingsensor array, which converts the imaged light into a digitalrepresentation of a portion of the scene. The substantially sphericallyshape of the arrangement of secondary lenses affords embodiments of thepresent invention the ability to mitigate the effects of field curvaturein the output of the objective lens.

An objective lens in accordance with the present invention ischaracterized by a layered structure that includes a spherical centrallens element and one or more spherically shaped lens shells, wherein allsurfaces have a common center of curvature. The lens shells are designedso that refraction at interior surface of the objective lens producesnegative spherical aberration that offsets the positive sphericalaberration introduced at the entry surface of the objective lens. Thespherically shaped lens shells further enable a reduction in themagnitude of each of chromatic and spherical aberrations in the outputof the lens. This reduces the magnitude of chromatic and sphericalaberration correction required by the secondary lenses in order toachieve a high-quality image of the scene at the sensor arrays. As aresult, the prescription of each secondary lens can be less severe,which, in turn, reduces the amount of coma and astigmatism introduced bythe secondary lenses into their respective image fields. In addition,simpler secondary lenses enable a smaller overall optical system volume.Further, a simpler prescription enables secondary lenses that are easierand cheaper to manufacture.

In some embodiments, the spherical central lens comprises a materialhaving a low refractive index and a high Abbe number. In someembodiments, the refractive index of the central lens material is withinthe range of approximately 1.28 to approximately 1.52. In someembodiments, the Abbe number of the central lens material is within therange of approximately 73 to approximately 96. In some embodiments, thecentral lens material is calcium fluoride.

An illustrative embodiment of the present invention comprises amonocentric objective lens, a plurality of secondary lenses, andplurality of sensors. The monocentric lens includes a substantiallyspherical central element and a plurality of spherically shaped shellelements, wherein the central element and shell elements are concentric.The central element comprises calcium fluoride, which provides apositive focusing power for the lens. In addition, calcium fluoride ischaracterized by low chromatic dispersion, which facilitates correctionof chromatic aberration. Each of the shell elements comprises a glasshaving an Abbe number that is lower than the Abbe number of the centralelement. The inclusion of the shell elements in the objective lensenables a reduction in the magnitude of both chromatic and sphericalaberrations in the output of the lens. In some embodiments, an air gapis included between two of the shell elements, which facilitatessimultaneous correction of chromatic and spherical aberration withoutintroducing significant dispersion.

In some embodiments, each secondary lens is paired with a differentsensor array to collectively define one of a plurality of substantiallyidentical sub-imaging units. The sub-imaging units collectively providea composite digital representation of the scene. In some embodiments,the sub-imaging units are arranged such that each image point isreceived by at least two secondary lenses so that the plurality ofsecondary lenses collectively provides an image of the scene that issubstantially free of blind spots.

An embodiment of the present invention comprises an optical system forproviding an image of a scene, the optical system comprising: (1) afirst lens comprising; (a) a first lens element that is substantially asphere having a center at a first position, wherein the first lenselement imparts a first aberration with a first magnitude on light thattransits the first lens element; (b) an entry lens shell having asubstantially uniform thickness and a center of curvature at the firstposition; and (c) an exit lens shell having a substantially uniformthickness and a center of curvature at the first position; wherein thefirst lens element, the entry lens shell, and the exit lens shellcollectively impart the first aberration with a second magnitude onlight that propagates through the first lens, and wherein the secondmagnitude is less than the first magnitude; and (2) a plurality ofsecond lenses that collectively image the scene through the first lens,wherein each of the plurality of second lenses has a unique opticalaxis.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic drawing of a multi-scale optical system inaccordance with an illustrative embodiment of the present invention.

FIG. 2 depicts operations of a method suitable for providing an image inaccordance with the illustrative embodiment of the present invention.

FIG. 3 depicts a schematic drawing of a cross-sectional view of anobjective lens in accordance with the illustrative embodiment of thepresent invention.

FIG. 4 depicts schematic drawing of a cross-sectional view of a camerain accordance with the illustrative embodiment of the present invention.

FIG. 5A depicts a modulation transfer function curve for a multi-scaleoptical system in accordance with the illustrative embodiment.

FIG. 5B-D depict spot size diagrams for system 100 at the surface of asensor array 106.

FIG. 6A depicts a schematic drawing of a side-view of a frame forholding a spherical arrangement of cameras in accordance with theillustrative embodiment of the present invention.

FIG. 6B depicts a receptor for receiving a camera in accordance with theillustrative embodiment of the present invention.

FIG. 7 depicts a schematic drawing of a cross-sectional view of anobjective lens in accordance with a first alternative embodiment of thepresent invention.

FIG. 8 depicts a schematic drawing of a cross-sectional view of a camerain accordance with the first alternative embodiment of the presentinvention.

FIG. 9A depicts a modulation transfer function curve for a multi-scaleoptical system in accordance with first alternative embodiment.

FIG. 9B-E depict spot size diagrams for an optical system comprisingobjective lens 700 and camera 800 at a sensor array 810.

FIG. 10 depicts a schematic drawing of a cross-sectional view of animaging system in accordance with a second alternative embodiment of thepresent invention.

FIG. 11 depicts modulation transfer function curves for optical system1000.

FIG. 12 depicts a schematic drawing of a cross-sectional view of anobjective lens in accordance with a third alternative embodiment of thepresent invention.

FIG. 13 depicts modulation transfer function curves for objective lens1202.

FIG. 14 depicts a schematic drawing of a cross-sectional view of anobjective lens in accordance with a fourth alternative embodiment of thepresent invention.

FIG. 15 depicts modulation transfer function curves for objective lens1402.

DETAILED DESCRIPTION

The following terms are defined for use in this Specification, includingthe appended claims:

-   -   Spherical is defined being characterized by (1) a common center        of curvature and (2) a uniform radius of curvature. A spherical        surface, for example, is a surface that has substantially the        same shape as at least a portion of a sphere.    -   Apochromatic is defined as focusing three or more wavelengths at        substantially the same focal distance or image field.

This invention is a continuation-in-part of parent case U.S. patentapplication Ser. No. 12/651,894 filed 4 Jan. 2010, entitled “Multi-scaleOptical System.”

As disclosed in the parent case, a multi-scale optical system comprisesa single objective lens and an array of small secondary lenses. Theobjective lens and the secondary lenses collectively image a scene ontoa plurality of sensor arrays, such as photodetector arrays, as aplurality of optical sub-images. Each secondary lens has a uniqueoptical axis and images a portion of the scene through the objectivelens to produce one of the optical sub-images. The sensor arrays convertthe plurality of optical sub-images into digital representations (i.e.,digital images) of portions of the scene. The plurality of digitalimages can then be combined to form a composite digital image of theentire scene.

The multi-scale imaging approach affords significant advantages overother imaging approaches. First, in a multi-scale imaging system, theobjective lens and secondary lenses split the task of imaging the scene.Light collection is done at the objective lens, which forms an aberratedimage at an image region. The secondary lenses are placed around thisimage region and each secondary lens relays a portion of the aberratedimage to form its optical sub-image at its corresponding planar sensorarray. In addition to relaying a portion of the aberrated image, eachsecondary lens processes the light by at least partially correcting itsrelayed portion of the aberrated image (i.e., reduces the magnitude ofat least one aberration). This separation enables each of the collectingand processing functions to be individually improved withoutsignificantly comprising the design of the other. It also enables alarge-scale objective lens to be used with a large-count multi-aperturearray, thereby reducing the trade-off between geometric aberration andfield-of-view.

In addition, the multi-scale imaging approach enables two adjacentsecondary lenses to gather rays from the same image point by locatingthe secondary lenses at positions displaced from the image field butnear one another laterally. Such an arrangement enables light from agiven point image to always be captured by at least one secondary lens.As a result, blind spots due to lateral spacing between adjacent sensorarrays are avoided.

As discussed in the parent application to this case, U.S. patentapplication Ser. No. 12/651,894, which is incorporated herein byreference, prior-art imaging systems have been demonstrated that includesecondary lenses that provide a degree of compensation for fieldcurvature. Such prior-art imaging systems include, for example, thosedisclosed by J. A. Cox, et al., in U.S. Pat. No. 6,556,349, issued Apr.29, 2003. Field curvature, however, is a global aberration. For thepurpose of this Specification, including the appended claims, a “globalaberration” is defined as an aberration that extends, in slowly varyingfashion, across multiple optical fields. A “localized aberration” isdefined as an aberration, or a portion of a global aberration, that issubstantially unique to an individual optical field. For example, aplurality of localized aberrations might collectively define a globalaberration; however, the magnitude of wavefront distortion associatedwith each localized aberration is substantially unique to its associatedindividual optical field.

Second, the secondary lenses can include a degree of wavefrontcorrection to correct aberrations introduced by the large-scaleobjective lens. This reduces the design complexity required for theobjective lens. This also enables faster collection optics, whichreduces overall system volume.

Third, multi-scale imaging is capable of improved image resolution.

Fourth, manufacturing cost and complexity can be significantly lower fora multi-scale imaging system. Smaller lenses are better at providingwavefront correction because: 1) wavefront correction and imageformation both yield geometric solutions with less wavelength-scaleerror over smaller apertures; and 2) manufacturing of complex lenssurfaces is much easier in smaller scale systems.

Fifth, in some multi-scale imaging systems, the secondary lenses aredesigned to focus at diverse ranges with overlapping fields. Thisenables tomographic object reconstruction by combining multi-scaleimaging with multi-dimensional image capture, such as, for example, in aTOMBO-based system (Thin Observation Module by Bound Optics).

Finally, multi-scale design enables the use of multiple discrete focalplane arrays. As a result, the discrete focal plane arrays can bearranged in any advantageous manner, including non-planararrangements—for example, an arrangement that matches the shape of theimage field of the objective lens. Further, the size of the focal planearrays can be selected at a granularity that reduces fabrication costand increases overall reliability. Still further, the sub-images fromthe plurality of focal plane arrays can be collectively synthesized intoa spatially correlated image of a scene without the stitching and fielduniformity issues found in prior-art imaging systems. And still further,the complexity of the post-processing required to synthesize thefull-scene image is significantly lower for embodiments of the presentinvention than the computational post-processing required in prior-artimaging systems, such as a TOMBO-based system.

The present invention enables an improved multi-scale optical system byemploying a monocentric lens as the objective lens. Monocentric lensesin accordance with the present invention include a central sphericallens element that interposes an entry lens shell and an exit lens shell.

FIG. 1 depicts a schematic drawing of a multi-scale optical system inaccordance with an illustrative embodiment of the present invention.System 100 comprises objective lens 102, secondary lenses 104-1 through104-5, and sensor arrays 106-1 through 106-5.

FIG. 2 depicts operations of a method suitable for providing an image inaccordance with the illustrative embodiment of the present invention.Method 200 begins with operation 201, wherein objective lens 102 isprovided.

Objective lens 102 is a monocentric lens suitable for collecting asufficient amount of light 110 received from scene 108. All opticalsurfaces of objective lens 102 have a center of curvature located atcenter point 112.

A monocentric lens is a lens wherein all surfaces of the lens share acommon center of curvature. Monocentric lenses identically focus lightcoming from any direction. This enables a monocentric lens to be usedfor very wide-field viewing. The image formed is spherically shapedrather than plane-shaped, and has unit angular magnification. Because ofthe symmetry of a monocentric lens, aberrations introduced by the lensare independent of the field point. As a result, a monocentric lensintroduces significant amounts of only spherical aberration into lightthat passes through the lens (neglecting image curvature and imagedistortion). The introduced aberrations are substantially limited tospherical aberration because it is the only aberration that isindependent of field point.

An example of a monocentric lens found in the prior art is the “Luneberglens,” which is described in Luneburg, R. K. (1944) Mathematical Theoryof Optics, Providence, R.I.: Brown University: pp. 189-213; Morgan, S.P. (1958) Journal of Applied Physics 29: pp. 1358-1368; and Doric, S.Munro, E. (1983) Journal of the Optical Society of America 73: pp.1083-1086; and Southwell, W. H. (1977) Journal of the Optical Society ofAmerica 67: pp. 1010-1014. The Luneburg Lens comprises a sphericallyshaped, gradient-index lens that forms images of objects on its surface.The Luneburg lens has been fabricated for operation at microwavefrequencies. The Luneburg lens is unsuitable for optical wavelengths,however, for several reasons. First, the Luneburg lens uses gradedrefractive indices from 1 to √2. Excluding exotic meta-materials,glasses are not available within this range of refractive indices.Second, practical gradient-index lenses are difficult to fabricate.Third, gradient-index lenses suffer from severe chromatic aberration andtherefore are unsuitable for imaging with broadband light.

In contrast to the Luneburg lens, objective lenses in accordance withthe present invention comprise a layered structure that:

-   -   i. achieve nearly diffraction-limited performance; or    -   ii. have a large field-of-view; or    -   iii. are apochromatic within the wavelength range from        approximately 450 nanometers (nm) to approximately 700 nm; or    -   iv. mitigate chromatic and/or spherical aberration; or    -   v. are capable of resolving greater than 10⁹ spots; or    -   vi. are practical to fabricate; or    -   vii. any combination of i, ii, iii, iv, v, and vi.

FIG. 3 depicts a schematic drawing of a cross-sectional view of anobjective lens in accordance with the illustrative embodiment of thepresent invention. Objective lens 102 is a multi-element monocentriclens comprising lens element 302, entry lens shell 304, and exit lensshell 306. FIG. 3 is described herein with continuing reference to FIGS.1 and 2.

Lens element 302 comprises hemispheres 308 and 310. Each of hemispheres308 and 310 comprise calcium fluoride. As a result, lens element 302 ischaracterized by a refractive index of approximately 1.433848 and anAbbe number of approximately 95.232905. Calcium fluoride ischaracterized by low chromatic dispersion; therefore, use of calciumfluoride in lens element 302 facilitates chromatic aberration correctionin multi-scale optical system 100. Although calcium fluoride is apreferred material for lens element 302, in some embodiments, lenselement 302 comprises a different material having a refractive indexwithin the range of approximately 1.28 to approximately 1.52. Materialssuitable for use in lens element 302 include, without limitation,calcium fluoride, fused silica, BK-7 glass, SK-7 glass, fluorocrownglass, magnesium fluoride, plastics, water, and perfluorooctane. In someembodiments, the material of lens element 302 is selected such that it'srefractive index is lower than the refractive index of the materials ofeach of entry lens shell 304 and exit lens shell 306 and, further, suchthat its Abbe number is higher than the Abbe number of the materials ofeach of entry lens shell 304 and exit lens shell 306.

Hemispheres 308 and 310 are joined at a central plane comprising centerpoint 112 to collectively define a shape that is substantially a spherehaving a diameter of approximately 164.5 millimeters (mm). It should benoted that, in some embodiments, lens element 302 comprises optionalflat region 312 to facilitate its mounting. In some embodiments,hemispheres 308 and 310 are sculpted so that they substantially includeonly those portions of spherical surfaces 322 and 324 that interact withthe light that transits the lens element 302.

Although in the illustrative embodiment the curved surfaces ofhemispheres 308 and 310 have substantially the same radius of curvature,it will be clear to one skilled in the art, after reading thisSpecification, how to specify, make, and use alternative embodiments ofthe present invention wherein the radius of curvature of the curvedsurface of hemisphere 308 is different than the radius of curvature ofthe curved surface of hemisphere 310.

Hemisphere 308 comprises pedestal 314. Pedestal 314 is typically formedby grinding back or etching surface 316 of hemisphere 308 outside theregion of the pedestal to form relieved surface 318. Relieved surface318 is then coated with layer 320 so that pedestal 314 and layer 320collectively define an optical stop in the interior of lens 102. Layer320 is a layer of opaque or absorbing material disposed on relievedsurface 318 in conventional fashion. In some embodiments, the processused to form relieved surface 318 leaves the surface sufficiently opaqueto obviate layer 320.

When hemispheres 308 and 310 are joined to form lens element 302,surface 316 of hemisphere 308 and surface 322 of hemisphere 310collectively form a substantially continuous region of lens material. Asa result, surfaces 316 and 322 do not constitute optical surfaces forthe purpose of this description, since light that passes through themdoes not see a material change.

It should be noted that, although the spherical shape of lens element302 mitigates introduction of many aberrations on light 120 as ittransits the lens element, lens element introduces some sphericalaberration and chromatic aberration onto light 120. It is an aspect ofthe present invention, however, that by employing properly designed lensshells at the entry and exit points of lens element 302, the magnitudeof one or both of spherical and chromatic aberration introduced by lenselement 302 is reduced.

Entry lens shell 304 is a curved shell section having a substantiallyspherical shape. In other words, entry lens shell 304 is a portion of aspherical shell. Entry lens shell 304 comprises flint glass (e.g.,LASF46A) that is characterized by a refractive index of approximately1.903660 and an Abbe number of approximately 31.39976. Entry lens shell304 has a substantially uniform thickness between spherical surfaces 326and 328 of approximately 48.163 mm.

Exit lens shell 306 is a curved shell section having a substantiallyspherical shape. In other words, exit lens shell 306 is a portion of aspherical shell. Exit lens shell 306 comprises flint glass (e.g., BAF50)that is characterized by a refractive index of approximately 1.6827260and an Abbe number of approximately 44.503507. Exit lens shell 306 has asubstantially uniform thickness between spherical surfaces 330 and 332of approximately 54.344 mm.

Objective lens 102 is designed to be substantially achromatic forwavelengths within the range of approximately 500 nm to approximately600 nm. It has an effective aperture size of approximately 100 mm. Insome embodiments, the aperture size of objective lens 102 is within therange of approximately 50 mm to approximately 200 mm; however, it willbe clear to one skilled in the art, after reading this specification,how to specify, make, and use an objective lens having any practicalaperture size.

Further, one skilled in the art will recognize that the specific designparameters (e.g., materials, radius of curvature, thickness, refractiveindex, Abbe number, etc.) provided for the elements of objective lens102 provide only one potential combination of design parameters thatdefine a suitable lens design. For example, one skilled in the art willrecognize that the material choices made for the elements of lens 102could include any of, for example and without limitation, calciumfluoride, fused silica, BK-7 glass, SK-7 glass, fluorocrown glass,magnesium fluoride, or plastics. It will be clear, therefore, afterreading this Specification, that objective lenses with reduced sphericalaberration and/or reduced chromatic aberration and/or apochromaticismcan be achieved with different design parameters.

Still further, one skilled in the art will recognize that, althoughobjective lens 102 comprises only refractive surfaces, a monocentriclens in accordance with the present invention can include reflectivesurfaces (e.g., a catadioptric lens).

Table 1 below summarizes the design parameters for objective lens 102.

TABLE 1 Design parameters for a representative monocentric objectivelens. Semi- Radius Thickness Diameter (mm) (mm) Glass (Schott catalog)(mm) Conic K Comments 135.000 48.163 LASF46A (n = 1.903660, 128.990Objective entrance V = 31.39976) surface 86.737 86.837 CAF2 84.472Internal CAF2 (n = 1.433848, V = 95.232905) sphere Infinity 86.837 CAF245.551 Objective stop (n = 1.433848, V = 95.232905) position −86.83754.344 BAF50 82.251 (n = 1.682726, V = 44.503507) −141.181 158.819 Air129.673 Objective exit surface

The inclusion and design of entry lens shell 304 and exit lens shell 306in objective lens 102 enables entry lens shell 304, lens element 302,and exit lens shell 306 to collectively reduce the magnitude of each ofspherical aberration and chromatic aberration from the magnitude ofthese aberrations introduced by lens element 302 individually.

In addition, the spherical symmetry of optical surfaces 326, 328, 322,324, 330, and 332 results in lens 102 introducing only field-independentaberrations into light 114. The primary source of aberration introducedby a spherically symmetric lens, such as lens 102, arises from therefraction of light rays as they enter the front surface (i.e., opticalsurface 326) from free space. It is an aspect of the present inventionthat the layers of lens 102 are designed so that the collectiverefraction introduced at the rest of the optical surfaces (i.e., opticalsurfaces 328, 322, 324, 330, and 332) produce negative sphericalaberration that, at least partially, offsets positive sphericalaberration introduced at optical surface 326.

Further, although entry lens shell 304 and exit lens shell 306 arespherically symmetric, they comprise different materials and/or shellthickness. This enables aberration correction to be achieved with fewersurfaces.

Lens 102 forms an aberrated image of scene 108 at spherically shapedimage field 126.

At operation 202, each of secondary lenses 104 images one of sceneportions 122-1 through 122-5 through objective lens 102. Each ofsecondary lenses 104 is paired with one of sensor arrays 106-1 through106-5 (referred to, collectively, as sensor arrays 106) to collectivelydefine one of cameras 116-1 though 116-5 (referred to, collectively, ascameras 116). For example, secondary lens 104-2 and sensor array 106-2collectively define camera 116-2.

Each of secondary lenses 104 produces one of optical sub-images 124-1through 124-5 (referred to, collectively, as optical sub-images 124) atits corresponding sensor array 106. For example, secondary lens 104-3images scene portion 122-3 through objective lens 102 and forms opticalsub-image 124-3 at sensor array 106-3.

Cameras 116 are arranged in a substantially spherical arrangement havinga center of curvature at center point 112. As a result, secondary lenses104 and sensor arrays 106 are also arranged in substantially sphericalarrangements whose centers of curvature are center point 112. Eachcamera 116 has a unique optical axis 118 that passes through the centerof its secondary lens 104 and sensor array 106.

Secondary lenses 104 are arranged in an arrangement that issubstantially spherical and has a center of curvature substantiallylocated at center point 112. Each of secondary lenses 104 is displacedfrom image field 126 by distance d1. In addition, each of secondarylenses 104 is separated from nearest neighbors by distance d2. Distancesd1 and d2 are selected to enable light rays from each image point inscene 108 to be captured by at least one secondary lens 104. As aresult, the inclusion of blind spots in a composite image collectivelyformed by sensor arrays 106 is mitigated.

In some embodiments, secondary lenses 104 are arranged in a sphericalarrangement wherein each of secondary lenses 104 is not displaced fromimage field 126. In some embodiments, each of secondary lenses 104 islocated further to center point 112 than image field 126.

FIG. 4 depicts schematic drawing of a cross-sectional view of a camerain accordance with the illustrative embodiment of the present invention.Camera 116 comprises secondary lens 104, which comprises lens elements402, 404, 406, and 408. Secondary lens 104 is designed to provide anoptical sub-image 124 having a diameter within the range ofapproximately 3 mm to approximately 4 mm.

Because objective lens 102 is a monocentric lens, it producessubstantially the same aberrations for all imaged points. In addition,due to its monocentric nature, objective lens 102 produces little or nooff-axis aberrations, such as coma or astigmatism, which would requireindividual correction by different secondary lenses located at differentdistances off optical axis 128 of imaging system 100.

As a result, the same prescription can be used for each secondary lens104 without regard for the angle of incoming light into objective lens102. This affords embodiments of the present invention with significantadvantages. In particular, the fabrication cost for the secondary lensesis dramatically reduced since the same lens design can simply bereplicated. Further, packaging complexity is reduced since the samepackaging methodology can be used to align and secure each of secondarylenses 104. Still further, identical cameras 116 can be produced involume at lower cost.

Secondary lens 104 is an axially symmetric combination of lens elements.As a result, secondary lens 104 introduces off-axis aberrations to light114. Since secondary lens 104 is relatively small, however, fewer lenselements are required to correct the induced off-axis aberrations thanwould be required of an axially symmetric lens the size of the objectivelens. In addition, in some embodiments, the design of secondary lens 102includes aspheric surfaces, which enables the secondary lens to achievegood relay optical performance with fewer lens elements. The use of fewlens elements reduces overall system weight, system complexity, andcost.

In some embodiments, the lens elements included in secondary lens 104are amenable to mass production, such as plastic molding or glassmolding. As discussed above, these advantages are afforded by the use ofa multi-scale optical system design, which enables a trade-off betweensimplicity in the objective lens design vs. complexity of the secondarylens design. Complexity is better included in the secondary lens designsince it is easier and cheaper to fabricate small complex optics thanlarge complex optics.

Table 2 below summarizes the design parameters for secondary lens 104.

TABLE 2 Design parameters for a representative secondary lens. Semi-Radius Thickness Diameter (mm) (mm) Glass (Schott catalog) (mm) Conic KComments Infinity 2.118 F2 (n = 1.620040, V = 36.366491) 5.000 Start ofsecondary lens −29.250 26.713 Air 5.000 7.569 10.689 2.917 FK51 (n =1.486561, V = 84.467994) 5.000 −1.491 −6.724 5.009 Air 5.000 −3.189−1.661 1.895 F2 (n = 1.620040, V = 36.366491) 5.000 −1.967 Secondarylens stop position −3.944 1.093 Air 5.000 −2.893 3.402 6.572 FK51 (n =1.486561, 5.000 −2.893 V = 84.467994) −12.748 5.000 Air 5.000 −7.770 Endof secondary lens Infinity — Image Plane 1.717 Image Plane

Lens element 402 is a plano-convex lens having a diameter ofapproximately 10 mm. Lens element 402 comprises glass having arelatively high refractive index of approximately 1.6200040 and arelatively low Abbe number of approximately 36.366491.

Lens element 404 is a convex-convex lens having a diameter ofapproximately 10 mm. Lens element 404 comprises glass having arefractive index of approximately 1.486561 and an Abbe number ofapproximately 84.467994.

Lens element 406 is a concave-convex lens having a diameter ofapproximately 10 mm. Lens element 406 comprises the same glass used inlens element 402.

Lens element 408 is a convex-convex lens having a diameter ofapproximately 10 mm. Lens element 408 comprises the same glass used inlens element 404.

Housing 410 is a tube that comprises a material having a lowthermal-expansion coefficient. Materials suitable for use in housing 410include, without limitation, Invar, super Invar, titanium, Zerodur,fused silica, composite materials, and the like.

Housing 410 aligns and holds lens elements 402, 404, 406, and 408 viaprecision rails 412. Precision rails are micromachined silicon railsthat separate the lens elements by air gaps as shown in Table 2. In someembodiments, precision rails are conventionally fabricated rails thatcomprise a material having a low thermal-expansion coefficient.Collectively, lens elements 402, 404, 406, and 408 enable a secondarylens that images a field-of-view of approximately 1.6 degrees.

Housing 410 also comprises flange 414, which includes pins 416 and slots418. Pins 416 and slots 418 facilitate alignment of housing 410 withreceptor 604, as described below and with respect to FIGS. 6A and 6B.

At operation 203, each of sensor arrays 106 converts a received opticalsub-image into a digital image of a scene portion 122.

Each of sensor arrays 106 comprises a two-dimensional arrangement of 10million charge-coupled device (CCD) elements 502 having a size ofapproximately 1.5 microns. As a result, each camera 116 is capable ofproviding 10 million individual electrical signals that are based on theintensity of light from 10 million image points in scene 108. In otherwords, each camera 116 is a 10-megapixel camera. The total size ofsensor array 106 is suitable for completely sampling an opticalsub-image having a diameter within the range of approximately 3 mm toapproximately 4 mm.

In some embodiments of the present invention, each of sensor arrayscomprises a two-dimensional arrangement of another photosensitivedevice, such as a CMOS sensor, photodetector, avalanche photodiode, andthe like. It will be clear to one skilled in the art how to specify,make, and use sensor arrays 106.

Each of sensor arrays 106 is electrically coupled with image processor128 via communications bus 120. Image processor 128 is a conventionalimage processing system that receives electrical signals from each ofelements 502 and forms digital sub-images based on optical sub-images124.

At operation 204, image processor 128 forms a composite digital image ofscene 108 based on the plurality of digital sub-images.

In some embodiments, each of cameras 116 further comprises an automaticfocusing mechanism. In some embodiments, autofocus is performed by ahelical focusing arrangement or by translating sensor array 106 alongthe optical axis 118 of the camera. Autofocus capability enables someembodiments of the present invention to focus different portions ofscene 108 at different depths.

In some embodiments, each of cameras 116 comprises an optical filter,such as a polarization or color filter. As a result, such embodimentscomprise a capability for analyzing a portion of scene 108 by examiningthe polarization and/or spectral signature of that portion.

In the illustrative embodiment, secondary lenses 104 are relied upon tocorrect residual spherical aberration introduced by objective lens 102.In addition, secondary lenses 104 correct curvature-of-field of imagefield 126 to enable formation of optical sub-images at the flat sensorarrays 106. Further, in the illustrative embodiment, secondary lenses104 reduce the scale of the image provided by objective lens 102 inorder to accommodate gaps between sensor arrays 106.

FIG. 5A depicts a modulation transfer function curve for a multi-scaleoptical system in accordance with the illustrative embodiment. Plot 500depicts the modulation transfer function (MTF) curve for system 100 at asensor array 106.

FIG. 5B-D depict spot size diagrams for system 100 at the surface of asensor array 106.

FIG. 6A depicts a schematic drawing of a side-view of a frame forholding a spherical arrangement of cameras in accordance with theillustrative embodiment of the present invention.

Frame 600 is a substantially spherically shaped support that comprises5000 receptors 602 and 604 for mounting 5000 cameras 116. Frame 600 isanalogous to a portion of geodesic sphere dual, wherein the surface offrame 600 is partitioned into hexagonal cells (i.e., receptors 602) anda relatively smaller number (typically 12) of pentagonal cells (i.e.,receptors 604). While it is desirable to partition the sphere into facesas uniform as possible, a sphere with greater than 20 faces cannot betiled into completely uniform faces. This tiling of the surface of frame600 into receptors 602 and 604 results in a nearly uniform spacing ofcameras 116, however.

Frame 600 has a radius of approximately 300 mm and a center of curvaturelocated at center point 112. In some embodiments, frame 600 comprises alow-thermal-expansion material, such as Invar, super Invar, titanium,Zerodur, fused silica, composite materials, and the like. In someembodiments, frame 600 comprises a material whose coefficient of thermalexpansion is substantially matched to the material of housing 410.

Frame 600 comprises 4988 hexagonal receptors 602 and 12 pentagonalreceptors 604. When receptors 602 and 604 are fully populated withcameras 116, therefore, system 100 is capable of imaging 50 billionpixels. In some embodiments, the relative number of receptors 602 and604 is other than 4988 to 12. In some embodiments, the total number ofreceptors is other than 5000.

Although in the illustrative embodiment frame 600 predominantlycomprises hexagonally shaped receptors, it will be clear to one skilledin the art, after reading this Specification, how to specify, make, anduse alternative embodiments of the present invention wherein frame 600comprises a different arrangement of receptors having shapes other thanhexagons. For example, in some alternative embodiments, frame 600 is anicosadeltahedral solid that comprises receptors having the shape of asubstantially equilateral triangle. Some other examples of suitableconfigurations for frame 600 are disclosed by H. Kenner in “GeodesicMath and How to Use it,” published by University of California Press(1976), which is incorporated by reference herein.

FIG. 6B depicts a receptor for receiving a camera in accordance with theillustrative embodiment of the present invention. Receptor 602 comprisesthrough-hole 604, channel 606, and threaded holes 608. Receptor 604 isanalogous to receptor 602.

Through-hole 604 is dimensioned and arranged to receive housing 410 ofcamera 116 such that its optical axis 118 is substantially aligned withcenter point 112. Each receptor comprises a through-hole into whichhousing 410 is inserted. Housing 410 is moved laterally in through-hole604 until optical sub-image 124 is properly focused. Once housing 410 isin place, its position in through-hole 604 is fixed via set screws,UV-curable epoxy, thermo-set epoxy, or other conventional method. Insome embodiments, each receptor 602 has a cross-sectional area ofapproximately 48.2 mm².

Rotational alignment of sensor array 106 established by rotating housing410 about optical axis 118. Once sensor array 106 is rotationallyaligned, its position is fixed via screws inserted through holes 418that mate with threaded holes 608.

Pins 416 mate with channel 606 to center sensor array 106 on opticalaxis 118.

Frame 600, receptors 602, and housings 410 collectively enable anarrangement of the cameras 116 that generates a mosaic of sub-images ofscene 108. By virtue of this mosaic arrangement, embodiments of thepresent invention are afforded with several advantages over imagingsystems of the prior art. First, such an arrangement enables overlappingfields-of-view to be used, which relieves a significant constraint forprior-art imaging systems wherein the focal plane array that receives animage of a scene must comprise photodetectors that are immediatelyadjacent to one another. As a consequence, each of sensor arrays 106 canbe sized to optimize cost, yield, etc. Further, such an arrangement alsoenables the use of detector arrays that are different sizes, if desired.Still further, detector arrays 106 can be spaced to allow for theinclusion of electronics between them. Finally, by forming a mosaic ofsub-images, multiple-aperture cameras that jointly optimize physicalfiltering, sampling, and digital processing of the resultant images canbe used.

It should be noted that the arrangement of cameras depicted in FIG. 1shows secondary lenses 104 (and sensor arrays 106) that are quite widelyspaced apart from one another. The large spacing is merely for thepurposes of clarity. One skilled in the art will recognize, afterreading this Specification, that practical arrangements of secondarylenses 104 will typically include more secondary lenses that are spacedmore closely. In some embodiments, for example, each secondary lens 104images a field-of-view within the range of approximately 1 degree toapproximately 5 degrees. As a result, hundreds of secondary lenses andsensor arrays would be required to provide an image having a 120-degreeincluded angle. One skilled in the art will recognize, after readingthis Specification, that the field-of-view imaged by each secondary lensand the total field-of-view of system 100 are matters of design and canhave any practical value.

FIG. 7 depicts a schematic drawing of a cross-sectional view of anobjective lens in accordance with a first alternative embodiment of thepresent invention. Objective lens 700 comprises lens element 702, entrylens shell 704, and exit lens shell 706.

Objective lens 700 is analogous to objective lens 102.

Lens element 702 comprises hemispheres 708 and 710. Each of hemispheres708 and 710 comprise glass having a refractive index of approximately1.486561 and an Abbe number of approximately 84.467994.

Hemispheres 708 and 710 are joined at a central plane comprising centerpoint 112 to collectively define a shape that is substantially a spherehaving a diameter of approximately 156.42 mm.

Hemisphere 708 comprises pedestal 714. Pedestal 714 is analogous topedestal 314. Layer 320 is disposed on relieved surface 718.

Entry lens shell 704 is a curved shell section that is a portion of aspherical shell. Entry lens shell 704 comprises glass having arefractive index of approximately 2.022040 and an Abbe number ofapproximately 29.059788. Entry lens shell 704 has a substantiallyuniform thickness of approximately 56.792 mm.

Exit lens shell 706 is a curved shell section that is a portion of aspherical shell. Exit lens shell 706 comprises glass having a refractiveindex of approximately 1.66819 and an Abbe number of approximately44.961828. Exit lens shell 706 has a substantially uniform thickness ofapproximately 59.181 mm.

FIG. 8 depicts a schematic drawing of a cross-sectional view of a camerain accordance with the first alternative embodiment of the presentinvention. Camera 800 comprises lens elements 802, 804, 806, and 808,sensor array 810, and housing 812.

Lens element 802 is a plano-convex lens having a diameter ofapproximately 5 mm. Lens element 802 comprises glass having a refractiveindex of approximately 1.677900 and an Abbe number of approximately55.199566.

Lens element 804 is a convex-plano lens having a diameter ofapproximately 5 mm. Lens element 804 comprises glass having a refractiveindex of approximately 1.434250 and a relatively high Abbe number ofapproximately 94.953489.

Lens element 806 is a convex-convex lens having a diameter ofapproximately 5 mm. Lens element 806 comprises the same glass used inlens element 802.

Lens element 808 has a compound front surface and a concave back surfaceand has a diameter of approximately 5 mm. Lens element 808 comprises thesame glass used in lens element 804.

Objective lens 700 and camera 800 are designed to operate cooperativelyto produce optical sub-images having a diameter within the range ofapproximately 7 mm to approximately 8 mm.

Sensor array 810 is analogous to sensor array 106; however, sensor array810 has a size suitable for completely sampling an optical sub-imagehaving a diameter within the range of approximately 7 mm toapproximately 8 mm.

TABLE 3 Design parameters for objective lens 700 and camera 800. RadiusThickness Semi-Diam. (mm) (mm) Glass (Schott catalog) (mm) Conic KComments 135.000 56.792 LASF35 (11 = 2.022040, 128.212 Objective V =29.059788) entrance surface 78.208 78.208 FK51A 75.882 Internal FK51A (n= 1.486561, V = 84.467994) sphere Infinity 78.208 FK51A 39.813 Objectivestop (n = 1.486561, V = 84.467994) position −78.208 59.181 BAF13 74.114(n = 1.66819, V = 44.961828) −137.389 162.611 Air 125.621 Objective exitsurface 89.806 3.538 LAKN12 5.000 Start of microlens (n = 1.677900, V =55.199566) −21.746 26.434 Air 5.000 −1.092 14.612 3.978 FK56 5.000−4.310 (n = 1.434250, V = 94.953489) 2123.027 6.494 Air 5.000 Microlensstop position 19.622 7.348 LAKN12 5.000 (n = 1.677900, V = 55.199566)−21.569 3.580 Air 5.000 10.735 4.207 FK56 5.000 −10.122 (n = 1.434250, V= 94.953489) 3.006 6.000 Air 5.000 −0.919 End of microlens Infinity —Image Plane 3.622 Image Plane

FIG. 9A depicts a modulation transfer function curve for a multi-scaleoptical system in accordance with first alternative embodiment. Plot 900depicts the MTF curve for an optical system comprising objective lens700 and camera 800 at a sensor array 810.

FIG. 9B-E depict spot size diagrams for an optical system comprisingobjective lens 700 and camera 800 at a sensor array 810.

FIG. 10 depicts a schematic drawing of a cross-sectional view of animaging system in accordance with a second alternative embodiment of thepresent invention. System 1000 comprises objective lens 1002 and cameras1004-1 through 1004-5.

Objective lens 1002 is a monocentric lens comprising lens element 1006,entry lens shell 1008, and exit lens shell 1010. Objective lens 1002 hasan effective aperture of approximately 100 mm and achieves substantiallydiffraction-limited performance over a field-of-view of approximately120 degrees. Objective lens 1002 is substantially achromatic over awavelength range from approximately 450 nm to approximately 700 nm.

Lens element 1006 is analogous to lens element 302 described above andwith respect to FIG. 3. Like lens element 302, lens element 1006comprises calcium fluoride to exploit this material's low chromaticdispersion and provide positive focusing power for objective lens 1002.

Lens element 1006 comprises hemispheres 1012 and 1014. Hemispheres 1012and 1014 collectively form a shape that is substantially a sphere. Lenselement 1006 has a diameter of approximately 120 mm and includes anoptical stop located approximately at center point 112 of the lens.

Entry lens shell 1008 comprises shell layers 1016 and 1018, which are inphysical contact with each other. Shell layer 1018 is in physicalcontact with lens element 1006.

Shell layer 1016 is a curved shell section that is a portion of aspherical shell. Shell layer 1016 comprises glass having a refractiveindex of approximately 1.591965 and an Abbe number of approximately48.509579. Shell layer 1016 has a substantially uniform thickness ofapproximately 17.043 mm.

Shell layer 1018 is a curved shell section that is a portion of aspherical shell. Shell layer 1018 comprises glass having a refractiveindex of approximately 1.753930 and an Abbe number of approximately52.270764. Shell layer 1018 has a substantially uniform thickness ofapproximately 44.792 mm.

Exit lens shell 1010 comprises shell layers 1020 and 1024, which areseparated by a air gap 1022, which has a substantially uniform thicknessof approximately 12.291 mm.

Shell layer 1020 is a curved shell section that is a portion of aspherical shell. Shell layer 1020 comprises glass having a refractiveindex of approximately 1.772500 and an Abbe number of approximately49.620227. Shell layer 1020 has a substantially uniform thickness ofapproximately 16.213 mm.

Shell layer 1022 is a curved shell section that is a portion of aspherical shell. Shell layer 1022 comprises glass having a refractiveindex of approximately 1.640480 and an Abbe number of approximately59.749915. Shell layer 1022 has a substantially uniform thickness ofapproximately 42.171 mm.

The inclusion of air gap 1022 between shell layers 1020 and 1024 enablessubstantially control of spherical aberration correction that issubstantially independent from control of chromatic aberrationcorrection. Spherical aberration control can be implemented bycontrolling the thickness of air gap 1022, which is inherentlyachromatic.

Objective lens 1002 produces an image at spherically shaped image field1026.

Each of cameras 1004-1 through 1004-5 (referred to, collectively, ascameras 1004) comprises a secondary lens 1028 and a sensor array 1030.Cameras 1004 are arranged in a substantially spherically shapedarrangement, centered at center point 112, such that each of secondarylenses 1028 is located at image field 1026.

Sensor array 1030 is analogous to sensor array 106 described above andwith respect to FIG. 1. Conventional packaging for a sensor array, suchas sensor array 1030 includes an optical window located above the arrayof sensors. In the illustrative embodiment, secondary lens 1028 isformed by polishing the outward surface of the sensor package window toform a concave lens having a radius-of-curvature of approximately101.810 mm (wherein the window comprises BK7 glass).

Secondary lens 1028 provides curvature-of-field correction over theincluded angle of the field-of-view of camera 1004. Typically thefield-of-view of each of cameras 1004 is approximately 4 degrees;however, it will be clear to one skilled in the art, after reading thisspecification, how to specify, make, and use alternative embodiments ofthe present invention wherein cameras 1004 have any practicalfield-of-view.

Table 4 below summarizes the design parameters for system 1000.

TABLE 4 Design parameters for a optical system 1000. Semi- RadiusThickness Diameter (mm) (mm) Glass (Schott catalog) (mm) Comments120.000 17.043 KZFS6 114.143 (n = 1.591965, V = 48.509579) 102.95744.792 LAK33A 98.582 (n = 1.753930, V = 52.270764) 58.165 58.165 CAF257.172 Internal CAF2 (n = 1.433848, V = 95.232905) sphere Infinity58.165 CAF2 37.271 Stop position (n = 1.433848, V = 95.232905) −58.16516.213 LAF34 56.264 (n = 1.772500, V = 49.620227) −74.377 12.291 Air70.830 −86.669 42.171 LAKL21 81.112 (n = 1.640480, V = 59.749915)−128.840 150.147 Air −101.810 1.000 BK7 10.0 Field curvature (n =1.516800, V = 64.167336) corrector Infinity 0.500 Air 10.0 windowInfinity — Image Plane 10.0 20 mm diagonal sensor

Secondary lens 1028 provides curvature-of-field correction over theincluded angle of the field-of-view of camera 1004. Typically thefield-of-view of each of cameras 1004 is approximately 4 degrees;however, it will be clear to one skilled in the art, after reading thisspecification, how to specify, make, and use alternative embodiments ofthe present invention wherein cameras 1004 have any practicalfield-of-view.

FIG. 11 depicts modulation transfer function curves for optical system1000. Plot 1102 depicts the MTF curve at a single 8-mm sensor array1030, wherein secondary lens 1028 has an approximately 8 degreefield-of-view. Plot 1104 depicts the MTF curve for optical system 1000for a field-of-view of up to approximately 60 degrees off-axis fromoptical axis 128.

FIG. 12 depicts a schematic drawing of a cross-sectional view of anobjective lens in accordance with a third alternative embodiment of thepresent invention. Objective lens 1202 is a monocentric lens comprisinglens element 1204, entry lens shell 1206, and exit lens shell 1208.Objective lens 1202 is analogous to objective lens 1002, but has aneffective aperture that is less than 100 mm. Objective lens 1202 issuitable for use in an optical system analogous to optical system 1000.

Lens element 1204 comprises hemispheres 1210 and 1212, each of whichcomprises calcium fluoride. Hemispheres 1210 and 1212 collectively forma shape that is substantially a sphere. Lens element 1204 has a diameterof approximately 33 mm and includes an optical stop locatedapproximately at center point 112 of the lens.

Entry lens shell 1206 is a curved shell section that is a portion of aspherical shell. Entry lens shell 1206 comprises glass having arefractive index of approximately 1.696732 and an Abbe number ofapproximately 56.420174. Entry lens shell 1206 is in physical contactwith lens element 1204 and has a substantially uniform thickness ofapproximately 23.457 mm.

Exit lens shell 1208 comprises shell layers 1216 and 1220, which areseparated by air gap 1218, which has a substantially uniform thicknessof approximately 4.076 mm.

Shell layer 1216 is a curved shell section that is a portion of aspherical shell. Shell layer 1216 comprises glass having a refractiveindex of approximately 1.835010 and an Abbe number of approximately43.129044. Shell layer 1216 has a substantially uniform thickness ofapproximately 5.053 mm.

Shell layer 1220 is a curved shell section that is a portion of aspherical shell. Shell layer 1220 comprises glass having a refractiveindex of approximately 1.640480 and an Abbe number of approximately59.749915. Shell layer 1220 has a substantially uniform thickness ofapproximately 42.171 mm.

Objective lens 1202 produces an image at spherically shaped image field1222. In similar fashion to optical system 1000, objective lens 1202 issuitable for use with a plurality of cameras (analogous to cameras1004), located at image field 1222, used to relay image portions of ascene through objective lens 1202.

Table 5 below summarizes the design parameters for objective lens 1202.

TABLE 5 Design parameters for objective lens 1202. Semi- RadiusThickness Diameter (mm) (mm) Glass (Schott catalog) (mm) Comments 40.00023.457 LAK31 38.021 (n = 1.696732, V = 56.420174) 16.543 16.543 CAF216.384 Internal CAF2 (n = 1.433848, V = 95.232905) sphere Infinity16.543 CAF2 12.140 Stop position (n = 1.433848, V = 95.232905) −16.5435.053 LASF41 16.223 (n = 1.835010, V = 43.129044) −21.596 4.076 Air20.855 −25.671 7.998 PK1 24.307 (n = 1.503781, V = 66.921827) −33.66945.508 Air

FIG. 13 depicts modulation transfer function curves for objective lens1202. Plot 1202 depicts the MTF curve using a single 10-mm sensor arraywith a secondary lens for providing curvature-of-field correction,wherein the secondary lens has an approximately 6 degree field-of-view.Plot 1204 depicts the MTF curve for objective lens 1202 (and suitablesecondary lenses) for a field-of-view of up to approximately 60 degreesoff-axis from optical axis 128.

FIG. 14 depicts a schematic drawing of a cross-sectional view of anobjective lens in accordance with a fourth alternative embodiment of thepresent invention. Objective lens 1402 is a monocentric lens comprisinglens element 1404, entry lens shell 1406, and exit lens shell 1408.Objective lens 1402 is analogous to objective lens 1002, but has aneffective aperture that is less than 75 mm. Objective lens 1402 issuitable for use in an optical system analogous to optical system 1000.

Lens element 1404 comprises hemispheres 1410 and 1412, each of whichcomprises calcium fluoride. Hemispheres 1410 and 1412 collectively forma shape that is substantially a sphere. Lens element 1404 has a diameterof approximately 23 mm and includes an optical stop locatedapproximately at center point 112 of the lens.

Entry lens shell 1406 is a curved shell section that is a portion of aspherical shell. Entry lens shell 1406 comprises glass having arefractive index of approximately 1.696732 and an Abbe number ofapproximately 56.420174. Entry lens shell 1406 is in physical contactwith lens element 1404 and has a substantially uniform thickness ofapproximately 8.358 mm.

Exit lens shell 1408 is a curved shell section that is a portion of aspherical shell. Exit lens shell 1408 comprises glass having arefractive index of approximately 1.637750 and an Abbe number ofapproximately 42.410177. Exit lens shell 1408 is in physical contactwith lens element 1404 and has a substantially uniform thickness ofapproximately 9.53 mm.

Objective lens 1402 produces an image at spherically shaped image field1414. In similar fashion to optical system 1000, objective lens 1402 issuitable for use with a plurality of cameras (analogous to cameras1004), located at image field 1414, used to relay image portions of ascene through objective lens 1402.

Table 6 below summarizes the design parameters for objective lens 1402.

TABLE 6 Design parameters for objective lens 1402. Semi- RadiusThickness Diameter (mm) (mm) Glass (Schott catalog) (mm) Comments 20.0008.358 LAK31 19.024 (n = 1.696732, V = 56.420174) 11.642 11.642 CAF211.351 Internal (n = 1.433848, CAF2 V = 95.232905) sphere Infinity11.642 CAF2 6.343 Stop (n = 1.433848, position V = 95.232905) −11.6429.530 KZFS11 11.059 (n = 1.637750, V = 42.410177) −21.172 23.419 Air

FIG. 15 depicts modulation transfer function curves for objective lens1402. Plot 1402 depicts the MTF curve using a single 10-mm sensor arraywith a secondary lens for providing curvature-of-field correction,wherein the secondary lens has an approximately 8 degree field-of-view.Plot 1404 depicts the MTF curve for objective lens 1402 (and suitablesecondary lenses) for a field-of-view of up to approximately 60 degreesoff-axis from optical axis 128.

It is to be understood that the disclosure teaches just one example ofthe illustrative embodiment and that many variations of the inventioncan easily be devised by those skilled in the art after reading thisdisclosure and that the scope of the present invention is to bedetermined by the following claims.

What is claimed is:
 1. An optical system for providing an image of ascene, the optical system comprising: a first lens that is monocentricabout a first position, the first lens operative for forming anintermediate image of the scene at an image field; a plurality of secondlenses, each second lens of the plurality thereof having a uniqueoptical axis that intersects the first position, wherein at least one ofthe plurality of second lenses is operative for reducing the magnitudeof a first aberration; and a plurality of sensor arrays, each sensorarray of the plurality thereof comprising a plurality of sensorelements; wherein the first lens, the plurality of sensor arrays, andthe plurality of second lenses are arranged such that each second lensof the plurality thereof relays a portion of the intermediate image asan optical sub-image at a different one of the plurality of sensorarrays.
 2. The optical system of claim 1 wherein the first lens isprovided such that the first aberration is selected from the groupconsisting of spherical aberration and chromatic aberration.
 3. Theoptical system of claim 1 wherein the first lens comprises: a first lenselement that is spherical about the first position, the first lenselement including a first hemisphere having a first surface whose centerof curvature is located at the first position and a second hemispherehaving a second surface whose center of curvature is located at thefirst position; an entry lens shell; and an exit lens shell.
 4. Theoptical system of claim 3 wherein the first lens element introduces asecond aberration with a third magnitude on light that transits thefirst lens element, and wherein the first lens collectively introducesthe second aberration with a fourth magnitude on light that transits thefirst lens, and further wherein the fourth magnitude is less than thethird magnitude.
 5. The optical system of claim 4 wherein the first lensis provided such that the first aberration is spherical aberration andthe second aberration is chromatic aberration.
 6. The optical system ofclaim 3 wherein the first lens is provided such that the exit lens shellcomprises a first shell layer and a second shell layer, and wherein thefirst shell layer and second shell layer are separated by an air gap. 7.The optical system of claim 3 wherein the first lens is provided suchthat the first lens element, entry lens shell, and exit lens shell arecollectively apochromatic.
 8. The optical system of claim 3 wherein thefirst lens is provided such that the entry lens shell and exit lensshell are characterized by different refractive indices.
 9. The opticalsystem of claim 1 wherein each of the plurality of sensor arrays isoperative for converting an optical sub-image into a plurality ofelectrical signals.
 10. The optical system of claim 9 further comprisinga processor operative for forming a plurality of digital sub-images ofthe scene, wherein each of the plurality of sub-images is based on theplurality of electrical output signals received from a different one ofthe plurality of sensor arrays.
 11. The optical system of claim 10wherein the processor is further operative for forming a compositedigital representation of the scene based on the plurality of digitalsub-images.
 12. The optical system of claim 1 wherein each second lensof the plurality thereof has the same prescription.
 13. An opticalsystem for providing an image of a scene, the optical system comprising:a first lens that is operative for receiving light from the scene andforming an intermediate image of the scene at an image field that issubstantially spherical about a first position, the first lenscomprising a first lens element that is monocentric about the firstposition, wherein the intermediate image is characterized by a firstaberration having a first magnitude; a plurality of cameras, each cameracomprising a second lens and a sensor array that collectively define anoptical axis of the camera, each second lens being operative for (1)relaying a portion of the intermediate image to form an opticalsub-image at its respective sensor array and (2) at least partiallycorrecting the first aberration such that its respective opticalsub-image is characterized by a second magnitude that is lower than thefirst magnitude; wherein the plurality of cameras is arranged in anarrangement that is substantially spherical such that each optical axisincludes the first position.
 14. The optical system of claim 13 whereinthe first lens element is substantially a sphere having a center at afirst position, and wherein the first lens further comprises: an entrylens shell having a substantially uniform thickness and a center ofcurvature at the first position; and an exit lens shell having asubstantially uniform thickness and a center of curvature at the firstposition; wherein the first lens element interposes the entry lens shelland exit lens shell, and wherein the first lens element introduces thefirst aberration on light that transits the first lens element such thatthe first aberration has a third magnitude that is greater than thefirst magnitude; and wherein the entry lens shell and exit lens shellare collectively operative for reducing the magnitude of the firstaberration from the third magnitude to the first magnitude.
 15. Theoptical system of claim 14 wherein the first lens element introduces asecond aberration on light that transits the first lens element suchthat the second aberration has a fourth magnitude, and wherein the entrylens shell and the exit lens shell are further collectively operativefor reducing the magnitude of the second aberration from the fourthmagnitude to a fifth magnitude that is lower than the fourth magnitude.16. The optical system of claim 15 wherein the first aberration isspherical aberration and the second aberration is chromatic aberration.17. The optical system of claim 13 wherein the aberration is sphericalaberration.
 18. The optical system of claim 13 wherein the aberration ischromatic aberration.
 19. The optical system of claim 13 wherein thefirst lens has a first focal length for each of a first wavelength,second wavelength, and third wavelength.
 20. The optical system of claim13 wherein each second lens of the plurality of cameras has the sameprescription.